Undecidability of quantized state feedback control for discrete time linear hybrid systems

Authors:
Federico Mari;Igor Melatti;Ivano Salvo;Enrico Tronci
Affiliations:
Computer Science Department, Sapienza University of Rome, Italy;Computer Science Department, Sapienza University of Rome, Italy;Computer Science Department, Sapienza University of Rome, Italy;Computer Science Department, Sapienza University of Rome, Italy
Venue:
ICTAC'12 Proceedings of the 9th international conference on Theoretical Aspects of Computing
Year:
2012

Citing 14
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Abstract

We show that the existence of a quantized controller for a given Discrete Time Linear Hybrid System (DTLHS) is undecidable. This is a relevant class of controllers since control software always implements a quantized controller. Furthermore, we investigate the relationship between dense time modelling and discrete time modelling by showing that any Rectangular Hybrid Automaton (and thus, any Timed Automaton) can be modelled as a DTLHS.